The consistency and asymptotic normality of the MLE in the exponential random graph model with
the degree sequence for undirected one-model networks or the bi-degree sequence for directed one-mode networks
have been established recently [[1]}, [2]}, [3]}, [4]},
[5]}].
For the bipartite networks, the asymptotic theory for the MLE in the model (REF ) has not been explored.
The model is closely related to the Rasch model [[6]}] for dichotomous item response experiments, which assumes that
item \(i\)  correctly gives a response to subject \(j\)  with probability \(\exp ( \alpha _i - \beta _j )/(1+\exp ( \alpha _i - \beta _j))\) .
By assuming that all the parameters in the Rasch model are bounded, [7]}
proved the consistency and asymptotic normality of the MLE when the number of items and subjects goes to infinity simultaneously.
